1089-7798 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LCOMM.2017.2761337, IEEE Communications Letters Optimal Reception Delay in Diffusion-based Molecular Communication Bayram Cevdet Akdeniz, Ali Emre Pusane and Tuna Tu˘ gcu Abstract—This letter proposes a simple and novel method for mitigating inter-symbol interference (ISI) in molecular com- munication via diffusion (MCvD). In MCvD applications, the messenger molecules released from the transmitter need some time to reach the receiver. Therefore, the molecules absorbed at the beginning of a transmission interval can only belong to the previous transmissions. Therefore, if a receiver shifts its absorption interval, ISI can be potentially reduced. We find the optimal delay time that the receiver shifts its absorption interval both numerically and analytically to minimize the ISI in the channel. We demonstrate the improved performance of the proposed shift-τ method in molecular communication over conventional concentration shift keying modulation. The major benefits of the proposed method are its simplicity and applicability to many other schemes in the literature. I. I NTRODUCTION Molecular communication via diffusion (MCvD) is a new concept that deals with the communication of nanomachines by sending and receiving messenger molecules that move ac- cording to the nature of diffusion. In particular, the transmitter encodes its intended message using messenger molecules and the receiver decodes the message by observing (counting) these molecules. Since the channel is diffusive, it takes a relatively long time for the molecules to reach the receiver compared to other conventional communication systems. This results in many crucial problems in MCvD channels. One of the major problems is inter-symbol interference (ISI). The receiver decodes an intended symbol within a predetermined time interval called symbol slot. However, due to the diffusive nature of the channel, a significant number of the molecules are not captured during the intended symbol slot and cause ISI, which leads to an adverse effect on decoding the following symbols. This problem, very-well studied in the past for con- ventional communication systems, poses a great challenge to molecular communications. For example, concentration shift keying (CSK) is one of the widely-used modulation schemes in MCvD that encodes the intended symbol by the number of molecules. However, accumulation of the molecules due to ISI leads to an error floor in this modulation. In the molecular communication literature, there are many proposed solutions to overcome ISI. These solutions are gener- ally modulation-based or equalization-based. As a modulation- based solution, in [1], using two different molecule types for two consecutive transmission symbols is proposed to eliminate ISI partially. This approach is known as molecular concentra- tion shift keying (MCSK). Similarly, in [2], using different types of molecules as orthogonal channels are proposed to re- duce ISI. On the other hand, using different types of molecules can be considered as an additional cost, and the receiver needs to have two different types of receptors, which increases overall system complexity. In [3], an adaptive threshold is determined for each symbol using the previously observed number of molecules, which requires additional memory. Equalization can be categorized into two groups as transmitter-based and receiver-based. One of the transmitter- based equalization method is proposed in [4]. In this work, the authors propose sending A-type molecules followed by B-type molecules after a pre-determined delay. The receiver decodes the symbol by the difference of the numbers of A- type and B-type molecules that are received in the symbol slot. The release-time and number of B-type molecules are optimized to maximize the signal to interference ratio (SIR). Another transmitter-based method is proposed in [5], which uses ISI as a constructive component by adapting the number of released molecules so that the residual molecules lead to a beneficial effect on decoding of the following symbols. As a receiver-based equalization method, in [6], minimum mean square error (MMSE) and decision feedback equalizers as well as maximum likelihood sequence estimation methods are proposed for MCvD channel. In [7], decoding is achieved by considering the previous observed samples and increasing the sampling rate of the receiver to improve the performance. In addition to these methods to reduce ISI, various different approaches have been proposed to improve system perfor- mance. For instance, if a flow is available in the channel, then the speed of the molecules is increased, which leads to a reduction in the number of the redundant molecules. In [8] and [9], receiver designs are presented in diffusive channels with flow. In [10], symbol synchronization, which is generally assumed to be perfect in the literature, is achieved using an additional type of molecule and optimal symbol interval is determined using the observed samples using Maximum likelihood and some other sub-optimal solutions. The methods mentioned above to mitigate ISI either require different types of molecules (and hence different types of receptors), additional computational complexity, and memory at the nanomachines or are proposed for specific channels. In this paper, we propose a novel method, called shift-τ method, that does not require any additional cost over the conventional CSK modulation. The basic principle behind this method is as follows: at the beginning of each symbol slot, the transmitter releases molecules to transmit the intended symbol to receiver. In conventional CSK, during this symbol slot, the receiver counts the number of observed molecules and then makes a hard decision. On the other hand, some of these molecules comes from the previous symbols and leads to